Error correction circuit and method, and semiconductor memory device including the circuit

ABSTRACT

An error correction circuit, an error correction method, and a semiconductor memory device including the error correction circuit are provided. The error correction circuit includes a partial syndrome generator, first and second error position detectors, a coefficient calculator, and a determiner. The partial syndrome generator calculates at least two partial syndromes using coded data. The first error position detector calculates a first error position using a part of the partial syndromes. The coefficient calculator calculates coefficients of an error position equation using the at least two partial syndromes. The determiner determines an error type based on the coefficients. The second error position detector optionally calculates a second error position based on the error type.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of application Ser. No.11/776,727 filed on Jul. 12, 2007, which is hereby incorporated for allpurposes.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to error correction, and moreparticularly, to an error correction circuit, an error correctionmethod, and a semiconductor memory device including the error correctioncircuit.

This application claims the benefit of Korean Patent Application No.10-2006-0080854, filed on Aug. 25, 2006 in the Korean IntellectualProperty Office, the disclosure of which is incorporated herein in itsentirety by reference.

2. Description of the Related Art

With the increase in memory capacity of a semiconductor memory device,an error correction circuit which can recover an error in a memory cellis required. Conventional error correction circuits may be divided intocircuits using a redundant memory cell and circuit using error checkingand correction (ECC).

A semiconductor memory device including an error correction circuitusing a redundant memory cell includes normal memory cells and redundantmemory cells and replaces a defective memory cell having an error with aredundant memory cell when writing and/or reading data. The errorcorrection circuit using a redundant memory cell is usually used fordynamic random access memory (DRAM).

A semiconductor memory device including an error correction circuitusing ECC generates and stores redundant data (referred to as paritydata or syndrome data) and detects and corrects errors occurring in databits using redundant data. The error correction circuit using ECC isusually used for read-only memory (ROM) and especially used very oftenfor flash memory including electrically erasable and programmable ROM(EEPROM) cells.

FIG. 1 is a schematic block diagram of a semiconductor memory device 100including a conventional ECC circuit 120. The semiconductor memorydevice 100 includes a memory core 110, the ECC circuit 120, and a hostinterface and logic unit 130.

The memory core 110 is a block including a memory cell array for storingdata. The ECC circuit 120 includes an ECC encoder 121 and an ECC decoder123. The host interface and logic unit 130 performs data interfacebetween a host 200 (e.g., a controller in a mobile device) and thememory core 110. The host interface and logic unit 130 can transmit andreceive d-bit parallel data (where “d” is 2 or an integer greater than2) to and from the host 200.

The ECC encoder 121 receives k-bit data through the host interface andlogic unit 130, generates (n−k)-bit syndrome data using the receivedk-bit data, and adds the (n−k)-bit syndrome data to the k-bit data.Accordingly, n-bit data (which may be referred to as an ECC word)comprised of the received k-bit data and the (n−k)-bit syndrome data isinput into the memory core 110.

When data stored in the memory core 110 is output, an ECC word, which iscomprised of k-bit data and (n−k)-bit syndrome data, is read from thememory core 110. The ECC decoder 123 divides the ECC word bypredetermined pattern data, generates syndrome data, and determinesexistence or non-existence of an error using the syndrome data. When anerror is determined to exist, the ECC decoder 123 detects a position ofthe error, that is, a position of a bit having the error, and correctsthe error bit. The correction of the error bit may be carried out by anerror corrector included in a unit, e.g., the host interface and logicunit 130 within the semiconductor memory device 100 or by the host 200.

FIG. 2 is a timing diagram illustrating conventional error correction.The conventional error correction includes data read/syndromecalculation in a period Tt between times T0 and T1, coefficientcalculation in a period Tcoeff between times T1 and T2, and errorposition calculation in a period Tcse between times T2 and T3.

During the data read/syndrome calculation, an ECC word (i.e.,information data and syndrome data) is read from a memory cell array andpartial syndromes S₀ through S_(2n-1) are calculated. The dataread/syndrome calculation requires a predetermined read time Tt. Duringthe coefficient calculation, coefficients σ₀ through σ_(n) necessary forproducing an error position equation are calculated and a predeterminedcoefficient calculation time Tcoeff is required. During the errorposition calculation, the error position equation is solved to obtain asolution so that an error position is detected. The error positioncalculation requires a predetermined error position calculation timeTcse. Accordingly, an error correction cycle (or an ECC cycle)corresponds to the sum of the time periods Tt, Tcoeff, and Tcse, and isalmost always constant regardless of the number of error bits.

Known circuits and methods for multi-bit ECC have many disadvantages.For example, a conventional ECC decoder is designed and implementedbased on a maximum number of correctable error bits. A conventionalmulti-bit ECC decoder requires more processing time than single bit ECCdecoder. Moreover, the error correction cycle is directly related todata access time (the time for a host to read data from a semiconductormemory device). As a consequence, conventional multi-bit ECC circuitsand methods may result in significantly slower data read times frommemory. Faster multi-bit ECC circuits and methods are needed.

SUMMARY OF THE INVENTION

Embodiments of the present invention decrease data read time andincrease read performance by selectively performing alternative errorposition calculations based on a number of detected error bits.

An embodiment of the present invention provides an error correctioncircuit that includes: at least two error position detectors configuredto be operated in parallel and to have different error positioncalculation times; a determiner configured to determine an error type;and a main controller coupled to the at least two error positiondetectors and the determiner, the main controller configured todetermine a final error position based on the error type and an outputfrom the at least two error position detectors.

Another embodiment of the present invention provides a semiconductormemory device including the above-described error correction circuit.The semiconductor memory device may further include an error checkingand correcting (ECC) encoder configured to generate syndrome data basedon information data and to generate the error correction coded data byadding the syndrome data to the information data, and a memory corecoupled to the ECC encoder and configured to store the coded data.

Further embodiments of the present invention provide an error correctionmethod includes: reading coded data; calculating a plurality of partialsyndromes using the coded data; and calculating a plurality of bitposition equation coefficients using the plurality of partial syndromes.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features and advantages of the present inventionwill become more apparent by describing in detail exemplary embodimentsthereof with reference to the attached drawings in which:

FIG. 1 is a schematic block diagram of a semiconductor memory deviceincluding a conventional error checking and correction (ECC) circuit;

FIG. 2 is a timing diagram illustrating conventional error correction;

FIG. 3 is a block diagram of a semiconductor memory device according tosome embodiments of the present invention;

FIG. 4 is a logic diagram illustrating operation of the ECC encoder inFIG. 3, according to some embodiments of the present invention;

FIG. 5 is a flowchart of an error correction method according to someembodiments of the present invention; and

FIG. 6 is a timing diagram illustrating how error correction isperformed in a time domain, according to some embodiments of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention now will be described more fully hereinafter withreference to the accompanying drawings, in which embodiments of theinvention are shown. This invention may, however, be embodied in manydifferent forms and should not be construed as limited to theembodiments set forth herein. Rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art. In thedrawings, like numbers refer to like elements throughout.

It will be understood that when an element is referred to as being“connected” or “coupled” to another element, it can be directlyconnected or coupled to the other element or intervening elements may bepresent. In contrast, when an element is referred to as being “directlyconnected” or “directly coupled” to another element, there are nointervening elements present. As used herein, the term “and/or” includesany and all combinations of one or more of the associated listed itemsand may be abbreviated as “/”.

FIG. 3 is a block diagram of a semiconductor memory device 300 accordingto some embodiments of the present invention. The semiconductor memorydevice 300 includes a memory core 310, an error checking and correction(ECC) circuit 320, and a host interface and logic unit 330. ECC circuit320 is coupled between the memory core 310 and the host interface andlogic unit 330.

The memory core 310 includes a memory cell array for storing data. Thememory cell array may include, for example, electrically erasable andprogrammable read only memory (EEPROM) cells having a floating gate, butthe present invention is not restricted thereto.

The host interface and logic unit 330 performs control and buffering forinterface between a host 200 (e.g., a controller in a mobile device or acomputer) and the ECC circuit 320. The host interface and logic unit 330may include an error corrector (not shown) which corrects an error incoded data based on a result of error detection performed by the ECCcircuit 320.

The host interface and logic unit 330 may include memory (not shown)like static random access memory (SRAM). In this case, when the host 200writes data to the SRAM, the data is encoded by the ECC circuit 320 andthen recorded in the memory core 310 (e.g., a flash memory core).Thereafter, an error in data read from the memory core 310 is detectedand corrected by the ECC circuit 320 and error-corrected data is storedin the SRAM. As a result, the host 200 reads the error corrected datastored in the SRAM. The host interface and logic unit 330 can transmitand receive d-bit parallel data (where “d” is 2 or an integer greaterthan 2) from and to the host 200.

The ECC circuit 320 includes an ECC wrapper 410 coupled to an ECCencoder 420 and an ECC decoder 430. The ECC wrapper 410 receives k-bitinformation data (where “k” is 2 or an integer greater than 2) from thehost interface and logic unit 330. The ECC wrapper 410 then adds(n−k)-bit dummy data to the k-bit information data. “n−k” is 1 or aninteger greater than 1, and each bit of the dummy data has apredetermined logic value. The ECC wrapper 410 then outputs n-bit datain series or parallel to the ECC encoder 420. For example, the k-bitinformation data may be 4096 bits, the (n−k)-bit dummy data may be 53bits, and the n-bit data may be 4149 bits.

FIG. 4 is a logic diagram illustrating operation of the ECC encoder 420in FIG. 3, according to some embodiments of the present invention.Referring to FIG. 4, the ECC encoder 420 includes a syndrome generator421 and an exclusive OR (XOR) operator 423.

The syndrome generator 421 receives n-bit data from the ECC wrapper 410and divides the received n-bit data by predetermined data to generate(n−k)-bit remainder (or syndrome) data. The predetermined data istypically referred to as a generator polynomial G(x). The integer “n−k”is determined based on a maximum number of correctable error bits and/ora maximum number of detectable error bits.

The XOR operator 423 performs an XOR operation on the n-bit datareceived from the ECC wrapper 410 and the syndrome data to generaten-bit coded data. When the information data, the syndrome data, and thecoded data are represented with I(x), S(x), and C(x), respectively, therelationship among the data is expressed by Equation (1):

S(x)=Ix ^((n-k))(x) % G(x),

C(x)=x ^((n-k)) I(x)+S(x)=Q(x)G(x),  (1)

where x^((n-k))(x) is a value obtained by shifting the k-bit informationdata I(x) by (n−k) bits in a most significant bit (MSB) direction, %G(x) indicates modulo G(x), and Q(x) is a quotient when C(x) is dividedby G(x). When “n−k” is 53, G(x) is a 53rd-order polynomial and S(x) is a52nd-order polynomial.

The n-bit coded data (also referred to as an ECC word) is input to thememory core 310. A cell array area of the memory core 310 may be dividedinto an area for storing information data and an area for storingsyndrome data. Alternatively, the n-bit coded data may be stored in thememory cell array without identifying the information data area and thesyndrome data area.

When coded data stored in the memory core 310 is output, n-bit codeddata (including k-bit information data and (n−k)-bit parity data) isread from the memory core 310 and is then input to the ECC wrapper 410.The ECC wrapper 410 may buffer the n-bit coded data and output the n-bitcoded data to the ECC decoder 430.

The ECC decoder 430 determines whether an error bit exists in coded datareceived from the ECC wrapper 410 and also detects an error position,i.e., the position of the error bit. In alternative embodiments, the ECCdecoder 430 may also correct the error bit in the coded data based onthe detected error position. In such cases, an error corrector (notshown) may be included in the ECC decoder 430.

In the illustrated embodiment, the ECC decoder 430 includes firstthrough fourth partial syndrome generators 431, 433, 435, and 437, acoefficient calculator 441, a 1-bit error position detector 451, amulti-bit error position detector 452, an error determiner 442, and amain controller 443. The ECC decoder 430 may further include a paritychecker 444, which may be an even parity checker or an odd paritychecker.

The first through fourth partial syndrome generators 431, 433, 435, and437 are coupled to the coefficient calculator 441. The 1-bit errorposition detector 451 is coupled to the first syndrome generator 431 andthe main controller 443. The multi-bit error position detector 452 andthe error determiner 442 are each coupled to the coefficient calculator441 and the main controller 443.

Although the first through fourth partial syndrome generators 431, 433,435, and 437 are described as separate components, they can also becollectively described as a single partial syndrome generator havingmultiple partial syndrome outputs. The first through fourth partialsyndrome generators 431, 433, 435, and 437 divide n-bit coded dataoutput from the memory core 310 by their predetermined data,respectively, so as to generate partial syndromes S₁, S₃, S₅, and S₇.When the n-bit coded data output from the memory core 310 is representedwith R(x) and the predetermined data, i.e., partial generationpolynomials of the respective first through fourth partial syndromegenerators 431, 433, 435, and 437 are represented with m₁(x), m₃(x),m₅(x), and m₇(x), the relationship between the data is expressed byEquation (2):

S ₁(x)=R(x) % m ₁(x),

S ₃(x)=f{R(x) % m ₃(x)},

S ₅(x)=f{R(x) % m ₅(x)},

S ₇(x)=f{R(x) % m ₇(x)},  (2)

where S₁(x), S₃(x), S₅(x), and S₇(x) correspond to the partial syndromesS₁, S₃, S₅, and S₇ generated by the first through fourth partialsyndrome generators 431, 433, 435, and 437, respectively, and %indicates a modulo operation. As shown in Equation (2), S₁(x) may bedirectly calculated from R(x) % m₁(x). And, S₃(x) S₅(x) and S₇(x) may becalculated using R(x) % m₃(x), R(x) % m₅(x) and R(x) % m₇(x),respectively.

In addition, the relationship between the generation polynomial G(x) ofthe syndrome generator 421 included in the ECC encoder 420 and thepartial generation polynomials m₁(x), m₃(x), m₅(x), and m₇(x) of thefirst through fourth partial syndrome generators 431, 433, 435, and 437may be defined as Equation (3):

G(x)=m ₁(x)*m ₃(x)*m ₅(x)*m ₇(x),  (3)

where “*” indicates Galois multiplication. When G(x) is a 53rd-orderpolynomial and S(x) is a 52nd-order polynomial, m₁(x), m₃(x), m₅(x), andm₇(x) are each a 13th-order polynomial and S₁(x), S₃(x), S₅(x), andS₇(x) are each a 12th-order polynomial.

When the first through fourth partial syndromes S₁, S₃, S₅, and S₇ areall zero (0), no error exists in coded data. If any one or more of thefirst through fourth partial syndromes S₁, S₃, S₅, and S₇ is not 0, thenan error exists in at least one bit of the coded data. When an erroroccurs, the coefficient calculator 441 begins calculating coefficientsσ₁, σ₂, σ₃, and σ₄ of an error position equation using the partialsyndromes S₁, S₃, S₅, and S₇. Simultaneously, the 1-bit error positiondetector 451 begins calculating the position of a 1-bit error using onlythe first partial syndrome S₁. The 1-bit error position detector 451 maybe implemented by a simple circuit so that the 1-bit error positiondetector 451 completes its calculation before the multi-bit errorposition detector 452 can complete multi-bit error positioncalculations. Although the 1-bit position calculator 451 may completeits operation ahead of the coefficient calculator 441, the componentscan be said to operate in parallel because they begin operations atsubstantially the same time.

The error position equation has the reciprocal of an error bit as aroot. The relationship between the coefficients σ₁, σ₂, σ₃, and σ₄ ofthe error position equation and the partial syndromes S₁, S3, S₅, and S₇may be obtained using diverse algorithms. Equations (4) and (5) areexemplary error position equations that express the relationship.

Equation (4) is an example of the error position equation for 1-biterror correction:

σ₁ x+1=0,  (4)

where σ₁=S₁ and a reciprocal of a root satisfying first-order Equation(4) indicates a 1-bit error position.

Equation (5) is an example of the error position equation for 2-biterror correction:

σ₂ x ²+σ₁ x+1=0,  (5)

where σ₁=S₁, σ₂=(S₁ ³+S₃)/S₁, and a reciprocal of a root satisfyingsecond-order Equation (5) indicates a 2-bit error position.

For 3- or more-bit error correction, coefficients of the error positionequation may be calculated in a similar manner to that described above.

According to some embodiments of the present invention, the coefficientcalculator 441 calculates the coefficients σ₁, σ₂, σ₃, and σ₄ accordingto the error position equation which can correct a maximum of 4 bits oferror.

The error determiner 442 determines an error type based on thecoefficients σ₁, σ₂, σ₃, and σ₄ calculated by the coefficient calculator441. In particular, the error determiner 442 determines whether adetected error is a 1-bit error (i.e., a first error type) or amulti-bit error (i.e., a second error type). For example, when thecoefficient σ₁ of a first-order equation is not 0 and the coefficientsσ₂, σ₃, and σ₄ of other order equations are all 0, the error positionequation is a first-order equation and the number of error bits is 1. Ifthe coefficient σ₂ of a second-order equation is not 0 and thecoefficients σ₃, and σ₄ of third- and fourth-order equations are 0, theerror position equation is a second-order equation and the number oferror bits is 2.

When the error determiner 422 determines the presence of a 1-bit error,the position of the error bit is determined by the 1-bit error positiondetector 451. In this instance, the multi-bit error position detector452 may not be operated. A 1-bit error position calculated by the 1-biterror position detector 451 may be referred to as a first errorposition.

When the error determiner 422 detects the presence of multiple biterrors, the positions of error bits are determined by the multi-biterror position detector 452. Multi-bit error positions calculated by themulti-bit error position detector 452 may be referred to as second errorpositions.

The 1-bit error position detector 451 and the multi-bit error positiondetector 452 may detect the position of an error bit based on the errorposition equations.

The 1-bit error position detector 451 is a quick error positioncalculator that is optimized to 1-bit ECC and is an exclusive circuitfor 1-bit error detection. The 1-bit error position detector 451 detectsthe position of one bit having an error in n-bit coded data based on afirst-order error position equation, e.g., Equation (4). Since thecoefficient σ₁ of the first-order error position equation is the same asthe first partial syndrome S₁, the first-order error position equationcan be determined once the first partial syndrome S₁ is generated by thefirst partial syndrome generator 431, regardless of a result ofcalculation by the coefficient calculator 441. Accordingly, the 1-biterror position detector 451 may begin operation in parallel with thecoefficient calculator 441 once the first partial syndrome S₁ isgenerated.

The multi-bit error position detector 452 detects the positions of 2 ormore error bits using the coefficients σ1, σ₂, σ₃, and σ₄ calculated bythe coefficient calculator 441. According to some embodiments of thepresent invention, the multi-bit error position detector 452 is an errorposition calculator which can detect the positions of at least two errorbits and at most four error bits.

Multi-bit error position detector 452 can detect error positions usingerror position equations. In this case, it is necessary to solve ani^(th)-order error position equation (where i=1, 2, 3, or 4) accordingto the number of error bits. Since it is difficult to obtain a generalsolution of a fourth-order error position equation, a Chien searchalgorithm may be used to determine the roots of the polynomial. TheChien search algorithm makes use of the fact that the roots will bepowers of primitive element α. A test root can therefore be expressed asα-^(j) over the range of j=0 to j=(n−1):α-⁰, α-¹, α-², α-³ . . .α-^((n-1)). When α-^(j) satisfies an error position equation, the j^(th)bit is determined to have an error. This operation may be performed withrespect to each code of n size in order to determine whethersubstituting j (altering j over the range of 0 to n−1) into errorposition equation repeatedly as n times satisfies the equation.

The main controller 443 determines a final error bit position based onthe detection result of the 1-bit error position detector 451 (i.e., thefirst error position) or the detection result of the multi-bit errorposition detector 452 (i.e., the second error positions). The maincontroller 443 determines a final error bit position according to thefirst error position when the error determiner 422 determines the firsterror type and the main controller 443 determines final error bitpositions according to the second error positions, ignoring thedetection result of the 1-bit error position detector 451, when theerror determiner 422 determines the second error type. In addition, themain controller 443 may further refer to a signal output from the paritychecker 444 in order to more accurately determine existence ornon-existence of an error and an error position.

After the main controller 443 has determined a final error bit positionor positions, the main controller 443 may provide the determined finalerror bit position(s) to the host interface and logic unit 330. The hostinterface and logic unit 330 may then correct one or more bit errors byinverting a logic value of the one or more erroneous bits.

Alternatively, the host interface and logic unit 330 may transmit theerror position information and the n-bit coded data (or just the k-bitinformation data) to the host 200. In this instance, the host 200 maycorrect one or more errors by inverting a logic value of bits based onthe error bit position information from the main controller 443.

FIG. 5 is a flowchart of an error correction method according to someembodiments of the present invention. The error correction methodillustrated in FIG. 5 may be performed by the ECC circuit 320illustrated in FIG. 3. The error correction method will be describedwith reference to FIGS. 3 through 5 below.

Prior to operation 610, coded data is generated by combining syndromedata with information data, and the coded data has been stored in thememory core 310. In operation 610, the coded data is read from thememory core 310. In operation 620, first through fourth partialsyndromes S₁, S₃, S₅, and S₇ are generated using the coded data. Thecalculations in operation 620 may be performed by the first throughfourth partial syndrome generators 431, 433, 435, and 437.

In case of 1-bit error correction (i.e., 1-bit ECC), an error positioncan be immediately detected using only the first partial syndrome S₁.Accordingly, as soon as the first partial syndrome S₁ is calculated inoperation 620, the 1-bit error position detector 451 may begin tocalculate an error position in operation 621. The coefficient calculator441 may calculate coefficients of an error position equation inoperation 622, and operations 621 and 622 may be performedsimultaneously. After the coefficient calculator 441 completes thecalculation of the coefficients of the error position equation, an errortype is determined in operation 630 based on the coefficients calculatedin operation 630. The error determiner 442 may perform operation 630. Ifthe error type is determined as a 1-bit error, i.e., the first errortype, then the 1-bit error is corrected in operation 640 based on 1-biterror position information which has already been calculated inoperation 621. If the error type is determined as a multi-bit error,i.e., the second error type, then the multi-bit error detector 452 cancalculate multiple bit error positions in operation 650, and themultiple bit errors may be corrected in operation 660. The hostinterface and logic unit 330 and/or the host 200 may perform operations640 and 660.

Although the method illustrated in FIG. 5 is described above withreference to components illustrated in FIG. 3, other combinations ofcomponents may be used to implement the method, according to designchoice. Moreover, the method illustrated in FIG. 5 could be implementedin software or in a combination of hardware and software. Likewise, anyone or more functional components illustrated with reference to thesemiconductor memory device 300 in FIG. 3 could be implemented insoftware.

FIG. 6 is a timing diagram illustrating how error correction isperformed in a time domain, according to some embodiments of the presentinvention.

During the data read and syndrome calculation between times T0 and T1,an ECC word (i.e., information data and syndrome data) is read from amemory cell array, and partial syndromes S0, S₁, S2 . . . S2n−1 arecalculated. This operation requires a predetermined read time durationof Tt. However, according to some embodiments of the present invention,the coefficient calculation and 1-bit error position calculation aresimultaneously commenced at time T1.

An error type is determined based on calculated coefficients σ0 throughσn. If a 1-bit error is determined, then multi-bit error calculation isomitted. Accordingly, in case of 1-bit error, an ECC cycle may end attime T4. In such a case, the ECC cycle time corresponds to the sum oftime Tt for the data read and syndrome calculation and time Tcs1 for the1-bit error position calculation, i.e., Tt+Tcs1, which is much shorterthan time required in a case where two or more bit errors occur.

In the case of multi-bit error, the ECC cycle corresponds to“Tt+Tcoeff+Tcse.” However, since the ECC cycle for 1-bit errorcorrection in embodiments of the invention is greatly reduced comparedto a conventional ECC cycle, the average ECC cycle time may besignificantly less where there is a combination of multi-bit errors andsingle-bit errors.

In the above embodiments of the present invention, an error correctioncircuit including a calculator that exclusively calculates a 1-bit errorposition. In other words, errors are classified into 1-bit errors andmulti-bit errors. In an alternative embodiment of the invention, a oneor two bit error may be classified into a first error type, and a threeor more bit error may be classified into a second error type. In such anembodiment, when a one or two bit error occurs, the position(s) of errorbit(s) may be quickly detected using a 2-bit error position calculatorbased on Equation (5). When three or more bit errors occur, errorpositions may be detected using a multi-bit error position detector suchas multi-bit error position detector 452.

In further embodiments of the present invention, errors may beclassified into three or more types, e.g., a first error type, a seconderror type, and a third error type, and error position detectors foreach of the respective error types may be provided so that an errorposition is most quickly detected with respect to the first error typeand an error position is second most quickly detected with respect tothe second error type. The error position detectors for the respectiveerror types may be operated in parallel and may have different errorposition detection times.

According to embodiments of the present invention, multi-bit ECCperformance is maintained without additional parity data, and ECC for apredetermined (e.g., 1 or 2) or less number of error bits can be quicklydone. As a result, average ECC cycle time is reduced, and data readspeed is increased.

While the present invention has been shown and described with referenceto exemplary embodiments thereof, it will be understood by those ofordinary skill in the art that various changes in form and detail may bemade herein without departing from the spirit and scope of the presentinvention, as defined by the following claims.

What is claimed is:
 1. An error correction method comprising: readingcoded data; generating a plurality of partial syndromes using the codeddata; calculating first error bit position data using a portion of theplurality of partial syndromes; and calculating a plurality of bitposition equation coefficients using the plurality of partial syndromes.2. The method of claim 1, wherein the calculating first error bitposition data is performed at least partially concurrent with thecalculating the plurality of bit position equation coefficients.
 3. Themethod of claim 1, further comprising determining whether an error typeis a first error type or a second error type based on the plurality ofbit position equation coefficients.
 4. The method of claim 3 wherein thefirst error type is an error having a single bit error and the seconderror type is an error having multiple bit errors.
 5. The method ofclaim 3 wherein the first error type is an error having two or fewer biterrors and the second error type is an error having three or more biterrors.
 6. The method of claim 3, wherein the number of errors of thesecond error type is greater than that of the first error type.
 7. Themethod of claim 3 further comprising, if the error type is the firsterror type, correcting the coded data based on the first error positiondata.
 8. The method of claim 3 further comprising, if the error type isthe second error type, calculating second error bit position data basedon the plurality of bit position equation coefficients.
 9. The method ofclaim 8, wherein a first calculation time required for a first errorposition detector to the first error bit position data is less than asecond calculation time required for a second error position detector tocalculate the second error bit position data
 10. The method of claim 7further comprising correcting the coded data based on the second errorbit position data.
 11. An error correction method comprising: readingcoded data; generating a plurality of partial syndromes using the codeddata; S620 detecting a first error position using a portion of theplurality of partial syndromes; generating a corresponding plurality ofcoefficients using the plurality of partial syndromes; determining inrelation to the plurality of coefficients whether the coded dataincludes less than or equal to a number of errors, or more than thenumber of errors; correcting a first error using the detected firsterror position when the coded data includes less than or equal to thenumber of errors; and detecting a second error position using theplurality of coefficients and correcting the second error using thedetected second error position when the coded data includes more thanthe number of errors.